Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x-6y &= 5 \\ -2x+6y &= 6\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = -6y+6$ Divide both sides by $-2$ to isolate $x$ $x = {3y - 3}$ Substitute this expression for $x$ in the first equation. $4({3y - 3}) - 6y = 5$ $12y - 12 - 6y = 5$ Simplify by combining terms, then solve for $y$ $6y - 12 = 5$ $6y = 17$ $y = \dfrac{17}{6}$ Substitute $\dfrac{17}{6}$ for $y$ in the top equation. $4x-6( \dfrac{17}{6}) = 5$ $4x-17 = 5$ $4x = 22$ $x = \dfrac{11}{2}$ The solution is $\enspace x = \dfrac{11}{2}, \enspace y = \dfrac{17}{6}$.